Resource consumption

Rates of growth

Linear, exponential, geometric

Some resources are so abundant we don’t think about exhaustion

Al, Ca, Cl, H, Fe, Mg, N, O, K, Si, Na, S

We should be careful about alarms.

In 1930, it was stated that our resources of copper will last 30 more years.

In 2008 is was stated that our resources of copper will last 30 years.

Annual world production (tons/yr)

Use of materials by class (tons)

Sources of Energy

Sunwindwavehydrosolar thermalphotovoltaic

MoonTidal

Nuclear decay

Hydrocarbons

Energy use by source (ExoJoules/yr)

Global energy consumption by source

Global energy consumption by use

Types of Energy

Chemicalfossil fuels, batteries, refined materials

RadiationRF, microwave, infrared, optical, X-ray, gamma...

Thermalhigh grade and low grade heat

Electrical and Magneticstatic and oscillating fields

Mechanicalpotential and kinetic energy

Nucleardecay of unstable elements

Conversion

Energy can be converted from one form to another.

The efficiency, , tells us how well we convert (and how much is lost)

Losses

Energy conversion usually has low grade heat as a by-product, which is lost.

Exception is electrical to thermal, which has 100% efficiency

Refining of metals, for example, involves conversion of thermal or electrical energy to chemical energy. Theoretically that energy could be recovered by allowing the metal to oxidize again. But the effiency is too low to be useful.

Conversion Efficiencies

There are limits to the conversion efficiencies. Consider thermal to mechanical.

Carnot taught us that

where Tin is the temperature entering the heat engine and Tout is the exit temp.

Carnot Efficiency with 150 C output

Approximate efficiency factors

Conversion path Efficiency kg CO2/MJ

Fossil fuel to thermal (enclosed) 100 0.07

Fossil fuel to thermal (vented) 65-75 0.1

Fossil Fuel to electric 33-39 0.2

Fossil fuel to mechanical (steam turbine)

28-42 0.17

Fossil fuel to mechanical (gas turbine)

46-50 0.15

Electric to thermal 100 0.2

Electric to mechanical (elec motors)

85-93 0.23

Electric to chemical (battery) 80-90 0.24

Electric to EM radiation (incand lamp)

15-20 1.17

Electric to EM radiation (LED) 80-85 0.23

Light to electric (PV) 10-20 0

Water

Water and materials

Growth of natural materials (some irrigated, some not)

Cooling cycles (with evaporative loss)

Dust suppression

Washing

Water to produce energy

Energy source Water used (l/MJ)

Grid electricity 24

Industrial electricity 11

Energy direct from coal 0.35

Energy direct from oil 0.3

Reserves

a mineral Reserve, R, is that part of a known deposit that can be extracted legally and economically at the time it is determined.

Reserves are an economic construct, which change depending on economics, technology and legislation

The Resource Base is the real total. This includes things we don’t know how to extract and estimates unknown deposits.

Reserves vs. Resource BaseO

re G

rade

Rich

Lean

Geologic CertaintyCertain Uncertain

alreadyexploited

Reserves

ResourceBase

Increasedprospecting

Improvedminingtech

Reserve movement

Commodity price (increased prices, increases reserve)

Improved technology (increase reserve)

Production costs (increased costs, reduce reserve)

Legislation (can go either way)

Depletion (if production exceeds discovery, reduces reserve)

Time to Exhaustion

Balance between supply and demand

Suppose the reserve is R, measured in total tons of material

Let P be the production rate measured in tons per year.

The the static index of exhaustion, tex,s will be

tex,s = R/P

Dynamic Index

The static index of exhaustion assumes there is no growth.

Production rate can increase, for example.

If r is the rate of production increase per year, then the dynamic exhaustion is

Copper: dynamic and static indices

Market Efficiency

We are assuming an efficient market - the supply and demand are in balance

If demand increases, then technology/economics offset.

What happens if the market forces don’t work?

Market Breakdowns

Supply chain concentration

depend on a few countries/regions... if there are problems...

Cartel Action

Stock piling

Substitutions

Recycling

Real criticality issues

The criticality of a resource is actually more complicated.

The resource base is finite (although partly unknown). The reserves increase for a while and then decrease when prospecting is saturated.

The exploitation (production) begins to consume the reserve, reducing it.

At some point, the rate of production exceeds the rate of discovery. Then prices rise, and criticality is pending.

Rate

(to

ns/

year)

Time

Rate of discoveryProduction rate

Price

Indicators of criticality

Rate of growth of discovery falls below rate of growth of production

Production rate starts to decline

Minimum economic ore grade falls

Prices start to rise

Real curves are not smooth...

Production and discovery

Reserves

Exercise

Consider the following data about a resource (next slide).

Examine the trends (graph price, production and reserves vs time). What conclusions can you reach?

Calculate the static index of exhaustion. What does the result suggest about the reserves?

Resource data for exercise

Year Price ($/kg)World production (M-

tons/year)Reserves (M-

tons)

1995 2.93 9.8 310

1996 2.25 10.7 310

1997 2.27 11.3 320

1998 1.65 12.2 340

1999 1.56 12.6 340

2000 1.81 13.2 340

2001 1.67 13.7 340

2002 1.59 13.4 440

2003 1.78 13.9 470

2004 2.86 14.6 470

2005 3.7 14.9 470

2006 6.81 15.3 480